On the characterization of relativistic quantum field theories in terms of finitely many vacuum expectation values. II

The problem of uniqueness of monotone continuous linear extensions of $$T_{(2N)} = \{ 1,T_1 ,...,T_{2N} \} \in E'_{(2N)} = \prod\limits_{n = 0}^{2N} {E'_n } $$ is solved. A characterization of a relativistic QFT in terms of finitely many VEV's is derived. All results are illustrated by an explicit discussion of the extension problem for special cases ofT ₍₄₎={1,0,T ₂,T ₃,T ₄}. This discussion contains explicitly necessary and sufficient conditions onT ₍₄₎ for the existence of minimal extensions and some convenient sufficient conditions.